Stein’s Lemma for generalized skew-elliptical random vectors

Abstract

This paper generalizes Stein's Lemma recently obtained for elliptical class distributions to the generalized skew-elliptical family of distributions. Stein's Lemma provides a useful tool for deriving covariances between functions of component random variables. This Lemma has applications in finance, notably for portfolio selection and hence for the capital asset pricing model (CAPM), as well as technical applications such as the computation of moments. It also leads to important propositions concerning the mean and variance of generalized skew-elliptical variables.

Keywords:

• Density generator
• multivariate generalized skew elliptical distributions
• normal distributions
• spherical distributions
• Stein’s Lemma

Additional information

Funding

This research was supported by the Israel Science Foundation (Grant No. 1686/17).